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<p>This work presents the design of artificial neural network (ANN) with fractional-order (FO) dynamics. The “fractionality" is introduced in the ANN by two ways: replacing the classical integer-order (IO) derivative with Riemann–Liouville (RL) and Caputo definitions of FO derivative in the learning algorithm and replacing the conventional activation function by a 3-parameter Mittag–Leffler function (MLF), which is an eigen function of the FO initial-value theorem. This multilayer fractional-order artificial neural network (FANN) is used for capturing the dynamics of linear single-input-single-output (SISO) and multi-input-multi-output (MIMO) systems. The inclusion of FO dynamics in the FANN endows it with the memory feature. In case of MIMO systems, a single FANN is able to model the dynamics of all interacting loops. The performance of the designed FANN is compared with IOANN. It is shown that the proposed FANN outperforms the IOANN in modeling the dynamics of the linear systems. The FANN captures the models of these linear systems more accurately resulting in lower mean-squared-error (MSE) with a negligible increase in the time required for training.</p>

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Fractional-order artificial neural network models for linear systems

  • 期刊论文

  • 发表日期：

    2025年3月14日

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  • Manisha Joshi,
  • Savita R. Bhosale,
  • Vishwesh A. Vyawahare

摘要

This work presents the design of artificial neural network (ANN) with fractional-order (FO) dynamics. The “fractionality" is introduced in the ANN by two ways: replacing the classical integer-order (IO) derivative with Riemann–Liouville (RL) and Caputo definitions of FO derivative in the learning algorithm and replacing the conventional activation function by a 3-parameter Mittag–Leffler function (MLF), which is an eigen function of the FO initial-value theorem. This multilayer fractional-order artificial neural network (FANN) is used for capturing the dynamics of linear single-input-single-output (SISO) and multi-input-multi-output (MIMO) systems. The inclusion of FO dynamics in the FANN endows it with the memory feature. In case of MIMO systems, a single FANN is able to model the dynamics of all interacting loops. The performance of the designed FANN is compared with IOANN. It is shown that the proposed FANN outperforms the IOANN in modeling the dynamics of the linear systems. The FANN captures the models of these linear systems more accurately resulting in lower mean-squared-error (MSE) with a negligible increase in the time required for training.